Question

(a) A pyramid has a height of 458 ft and its base covers an area of 14.0 acres (see figure below). The volume of a pyramid is given by the expression where B is the area of the base and h is the height. Find the volume of this pyramid in cubic meters. (1 acre 43,560 ft) m3 What If? If the height of the pyramid were increased to 517 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase? (b)

Answer 1

a)

$V=Bh/3=14\times 43560\times 458/3=9.31\times 10^7\,ft^3$

In m^3 the answer is

$V=9.31\times 10^7\times (0.3048)^3=2.64\times 10^6\,m^3$

b) The new base would be

$B=517\times 14/458=15.8\,\,acre$

The new volume would be

$V'=15.8\times 43560\ties 517/3=1.19\times 10^8\,\,ft^3$

Percentage change is

$100(V'-V)/V=27.42\,\%$